# probability – Compute \$F_V(t)\$ – Mathematics Stack Exchange

Given $$f_{X,Y}(t)=left{begin{array}{rcl} 1/2& xin(-1,0),-1-xleq yleq1+x\1/2& xin(0,1),x-1leq yleq1-xend{array}right.$$
Compute $$F_V(t)$$ V=X-Y

I’ve tried using $$F_V(t)=int_{-infty}^{t}int_{-infty}^{infty}f(x+y,y)dydx$$ and got $$F_V(t)=left{begin{array}{rcl} frac{t^2+2t+2}{2}& tleq0\ frac{-t^2+2t+2}{2}& tgeq0end{array}right.$$
But in the answers the result is $$Vsim U(-1,1)$$